Semiconductor thin films with metallic inclusions display extraordinary magnetoresistance (EMR) at room temperature, with enhancements as high as 100%-750,000% at magnetic fields ranging from 0.05 to 4 Tesla. The magnetoresistance (MR) is defined as MR=[R(H)−R(0)]/R(0), where R(H) is the resistance at finite field, H. These enhancements have been shown on a composite van der Pauw disk of a semiconductor matrix with an embedded metallic circular inhomogeneity that was concentric with the semiconductor disk and for a rectangular semiconductor wafer with a metallic shunt on one side.
Magnetic materials and artificially layered metals exhibit giant magnetoresistance (GMR) and manganite perovskites show colossal magnetoresistance (CMR). However, patterned non-magnetic InSb shows a much larger geometrically enhanced extraordinary MR (EMR) even at room temperature.
In FIG. 1(a), the typical Hall bar configuration 10 is shown. In an applied magnetic field 14 the electrons have a circular trajectory around the lines of the magnetic field, as displayed in FIG. 1(b). As soon as the current begins to flow, the space charge accumulation on one side gives rise to a (Hall) electric field Ey20 which is measured by the voltage difference across the Hall bar, the Hall voltage. If one assumes only one type of carrier with a delta-function velocity distribution, the force on the carriers from the Hall field cancels the Lorentz force and the direct current jx22 continues to remain the same, as indicated in FIG. 1(c). There is then no magnetic field dependence of the resistance in this case, e.g. the MR, Δρ/ρ0=0 where ρ is the resistivity and ρ0 is the zero field resistivity.
In the Corbino disk, illustrated in FIG. 2, there are two concentric contacts 30 with the current entering at the inner contact and exiting at the outer contact. In the presence of a magnetic field 36 perpendicular to the Corbino disk the electron trajectories 34 follow circular paths and the resistance is a function of the magnetic field. Moreover, because the conducting electrodes are in this case equipotential surfaces, no space charge accumulates on them and no Hall voltage is developed. Since there is no Hall field to produce a force that competes with the Lorentz force there can be a large MR, which in this case is Δρ/ρ0=(μH)2 where μ is the carrier mobility and H is the applied magnetic field. The geometric differences in the standard Hall geometry and the Corbino geometry yield a significant field dependence of the resistance in the latter.
In the presence of metallic inhomogeneities narrow-gap semiconductors show marked enhancement of the MR. Because of their small carrier masses the narrow gap high mobility semiconductors such as InSb and HgCdTe are the preferred materials to consider.
Narrow gap semiconductors (NGS)are preferable since such materials have a high phonon-limited room-temperature carrier mobility, μ300. For instance, for bulk InSb μ300=7.8 m2/Vs, while for InAs (indium arsenide) μ300=3 m 2/Vs10. An additional advantage of NGS is its low Schottky barrier (W. Zawadzki, “Electron transport phenomena in small-gap semiconductors”, Adv. Phys. 23, 435-522 (1974)). This feature avoids the depletion of carriers in the semiconductor by the artificially-structured metallic inclusions and ensures good electrical contacts.
InSb is a favored material because of its higher mobility. However there is a problem associated with the growth of thin films of this material. InSb by itself cannot be used as a substrate in a magnetic sensor because of its very large parallel conductance. No other III-V binary compound or group IV substrate is lattice matched to InSb. Therefore GaAs (gallium arsenide) (lattice mismatch is 14%) is usually employed for reasons of cost and convenience.
Other possible materials include, but are not limited to, Si, GaAs, HgCd, Hg1-xCdxTe, InSb, InSbTe, InAs, InAsSb as single layered material or multi-layered material or a material from a mixture made of these materials. However, it is understood that any comparable material can be used.
Shown in FIG. 3(a) is a cylindrical metal (Au) 40 embedded within a semiconducting slab 42. The conductivities of the semiconductor and the metal are σS 44 and σM46, respectively, in the absence of a magnetic field. In low magnetic fields, the current flowing through the material is focused into metallic regions with the metal acting as a short circuit; the current density, j, is parallel to the local electric field Eloc as indicated in FIG. 3(b). For σM>>σS the surface of the metal is essentially an equipotential. Thus Eloc is normal to the interface between the metal and semiconductor.
At finite magnetic field, the current deflection due to the Lorentz force results in a directional difference between j and Eloc, the angle between them being the Hall angle. For sufficiently high fields the Hall angle approaches 90° in which case j is parallel to the semiconductor-metal interface and the current is deflected around the metal which acts like an open circuit as indicated in FIG. 3(c). The transition of the metal from a short circuit at low field to an open circuit at high field gives rise to the very large MR or EMR.
Under steady state conditions the problem of determining the current and the field in the inhomogeneous semiconductor reduces to the solution of Laplace's equation for the electrostatic potential. For some simple structures this problem can be solved analytically. In general, however, the location and material properties of the inhomogeneities can be altered and the semiconducting material can be shaped to enhance the MR. In order to have this freedom to explore the geometrical enhancement of the MR in the device and to be able to consider semiconductor films and metallic inclusions/shunts of arbitrary shape, a numerical approach to the simulation of the enhanced MR is required.